How do I create a clay/fingerprint texture on a Blender model (as shown in the art pieces here)?
I saw the happy globe on reddit:)
You can get a goot fingerprint texture for free from Poliigon.com.
https://www.poliigon.com/search?query=Fingerprints

You need to change the render engine to Cycles and create a material while you have an object selected.

Click the "use nodes" button and open the node editor (where the different modes can be chosen).

In the node editor press Shift+A and chose "Image Texture" from the menu. If you use the add-on "Node Wrangler", you can click on the image texture node and press Shift+T to get your mapping node.

You then choose the texture of the fingerprints in the image texture node. You got to create a bump node and plug in your image texture there and then plug the bump to the normal node of the shader you choose. I recommend the principled shader. You could also directly use the displacement node to plug in your image texture. In that case just put a math node in between them and choose the multiply function to control the strenght of the displacement. If you do that you can change to the experimental feature set in the render panel and then go to the Settings section of the material tab and change the material tab from bump to true. 

Don't forget to unwrap the mesh object you want to apply the texture on.
I hope this works for you as an explanation. It's a very broad question.